Winter weather affects asp viper (Vipera aspis) population dynamics through susceptible juveniles
Res Altwegg1
Department of Biology, University of Victoria, Victoria, British Columbia, V8W 3N5 Canada
Stefan Dummermuth
Weissensteinstrasse 111, CH-4515 Oberdorf, Switzerland
Bradley R. Anholt
Department of Biology, University of Victoria, Victoria, British Columbia, V8W 3N5 Canada
Thomas Flatt2
Department of Biology, Unit of Ecology and Evolution, University of Fribourg, Chemin du Musée 10, CH-1700 Fribourg, Switzerland
1Corresponding author. E-mail: altwegg@uvic.ca
2 Present address: Department of Ecology and Evolutionary Biology, Brown University, Box G-W, Providence, Rhode Island 02912, USA
1 Published in "Oikos 110 (1), 55-66, 2005"
which should be cited to reference this work.
Abstract
1
Detailed studies on mammals and birds have shown that the effects of climate variation 2
on population dynamics often depend on population composition, because weather affects 3
different subsets of a population differently. It is presently unknown whether this is also true for 4
ectothermic animals such as reptiles. Here we show such an interaction between weather and 5
demography for an ectothermic vertebrate by examining patterns of survival and reproduction in 6
six populations of a threatened European snake, the asp viper (Vipera aspis), over six to 17 years.
7
Survival was lowest among juvenile and highest among adult snakes. The estimated annual 8
probability for females to become gravid ranged from 26% to 60%, and was independent of 9
whether females had reproduced in the year before or not. Variation in juvenile survival was 10
strongly affected by winter temperature, whereas adult survival was unaffected by winter 11
harshness. A matrix population model showed that winter weather affected population dynamics 12
predominantly through variation in juvenile survival, although the sensitivity of the population 13
growth rate to juvenile survival was lower than to adult survival. This study on ectothermic 14
vipers revealed very similar patterns to those found in long-lived endothermic birds and 15
mammals. Our results thus show that climate and life history can interact in similar ways across 16
biologically very different vertebrate species, and suggest that these patterns may be very general.
17 18
Introduction
18
Stochastic variation in weather and climate increases the temporal variation in fitness 19
components, thereby affecting the dynamics and extinction risk of a population (Andrewartha and 20
Birch 1954, Lande 1993). Recent studies have revealed that weather does not affect all age 21
classes and both sexes in the same way (Leirs et al. 1997, Coulson et al. 2001). For example, 22
temperature fluctuations explained a large proportion of the variance in juvenile but not adult 23
survival in barn owls (Altwegg et al. 2003). The effect of environmental variability on 24
fluctuations in population numbers therefore critically depends on the demographic composition 25
of the population and the life history of the species (Sæther et al. 2002).
26
The effect of variation in a particular fitness component on variation in population 27
numbers depends on how sensitive the population growth rate is to changes in that component 28
(Caswell 2001). In large herbivores and long-lived birds, for example, the population growth rate 29
is least sensitive to variation in reproduction and survival of young individuals (Sæther 1997, 30
Gaillard et al. 2000). Yet, those fitness components that have the least effect on population 31
growth rate tend to be the most variable ones (Gaillard et al. 2000), whereas traits more closely 32
linked to population dynamics tend to be less variable (Sæther and Bakke 2000). This pattern 33
may be due to selection for reduced variance, acting most strongly on those traits that are closely 34
linked to fitness (Gillespie 1977, Stearns and Kawecki 1994, Pfister 1998).
35
Stochastic environmental factors may thus affect populations through complex 36
interactions with demography. However, only detailed individual-based studies of natural 37
populations can unravel such processes. Although such data sets have begun to accumulate for 38
large mammals and birds, where individuals can be followed relatively easily throughout their 39
lives (Gaillard et al. 1998, Sæther and Bakke 2000), there is almost no information on the 40
interplay between demography and environmental stochasticity in ectothermic vertebrates. Yet, 41
the insights gained from endothermic mammals and birds may not be readily applicable to 42
ectothermic vertebrates for two reasons. First, the activity patterns of ectotherms such as reptiles 43
and amphibians depend more on ambient temperature than those of mammals and birds. Second, 44
the low energy requirements make ectotherms less susceptible in terms of survivorship to long 45
periods of weather-caused food shortage (Pough 1980, Peterson et al. 1993). Thus, to understand 46
how weather affects fitness and population dynamics of ectothermic vertebrates, we need long- 47
term individual-based studies.
48
Here we illustrate the interaction between weather and demography in a threatened 49
ectothermic vertebrate, the asp viper (Vipera aspis L.). We monitored 415 individuals in six 50
populations located in the Jura mountains in northern Switzerland for 6 to 17 years (see also Flatt 51
and Dummermuth 1993, Flatt et al. 1997). First, we estimated age- and sex-specific survival rates 52
and the reproductive rate of females using capture-mark-recapture models (Lebreton et al. 1992).
53
Second, we used the same methods to relate temporal variation in these fitness components to 54
active-season and winter weather. Finally, we estimated the sensitivity of the population growth 55
rate to changes in each of the fitness components using matrix population models and calculated 56
the effects of weather-caused variation on population growth (Caswell 2001). Several studies 57
estimated survival rates in snakes (e.g. Saint Girons 1957, Viitanen 1967, Gregory 1977, Brown 58
and Parker 1984), and examined the effect of weather or climatic conditions on various aspects of 59
reptile ecology (e.g., Moser et al. 1984, Peterson et al. 1993, Daltry et al. 1998, Flatt et al. 2001, 60
Sun et al. 2001, Lourdais et al. 2004, and references therein). Our study extends these findings in 61
two important ways. First, we account for variation in detection probability, which is likely to be 62
lower for juvenile than for adult snakes, and may depend on the weather during the surveys.
63
Second, we explicitly model the life cycle of our study organism, and thus estimate the impact of 64
external factors (such as weather) on population dynamics through variation in a particular fitness 65
component. An explicit representation of the life cycle is necessary because similar changes in 66
two different fitness components will not necessarily have similar effects on overall fitness and 67
population dynamics (Ehrlén 2003).
68
Methods
69
Field methods 70
Between 1986 and 2002, we monitored six isolated populations of asp vipers. Flatt and 71
Dummermuth (1993) and Flatt et al. (1997) provide a description of the natural history of the asp 72
viper and methodological details of fieldwork. Sample sizes and short descriptions of the study 73
sites are given in Appendix I. We visited each site between one and 35 times per year during the 74
entire activity period, from mid-March to mid-October, but 74% of the observations were made 75
between Mai and September. Snakes were located from a distance with telephoto lenses, 76
binoculars or by sight while walking slowly through the terrain. Identification of known 77
individuals was based on photographs and detailed drawings of the head and neck coloration 78
made at first encounter. We used overall coloration, dorsal colour pattern, scars and other 79
distinctive marks for identification. In most cases, individuals were clearly identifiable from close 80
distance and were only hand-captured if their identity was in doubt (10-20% of the cases). For 81
each individual we recorded at every encounter the age class, sex, sight-estimated size, and 82
reproductive status for females. Gravid female asp vipers recognisably change their body 83
proportions within a few weeks after copulation. In doubtful cases, the snake was captured and its 84
reproductive status verified by hand-scanning the body. We avoided capture whenever possible in 85
order to minimise the disturbance of these threatened animals. Comparisons using captive 86
animals showed that our estimates of body size are within 10% of the measured size (SD, 87
unpublished data).
88
Age determination of individuals at first encounter was based on approximate body size.
89
We classified individuals smaller than 30 cm as juvenile, individuals between 30 and 50 cm as 90
subadult, and larger individuals as adult. In our populations, female vipers generally start 91
reproducing at 50 cm and in their 4th or 5th year (SD, personal observation). Males may start 92
reproducing earlier, but their reproductive status could not be assessed in the field. Since the 93
subadult stage usually takes three years to complete, we assigned individuals to yearly age classes 94
based on their size at first encounter, assuming similar growth rates among individuals over the 95
first four years of life (first year subadult: < 37 cm, second year: between 37 and 44 cm, third 96
year: > 44 cm). Growth may vary with food abundance, and our size estimates may be less 97
accurate than if we had been able to hand-measure each individual. We therefore estimated the 98
impact of potential errors in age determination on our survival estimates for population B, which 99
is the smallest population with age effects, and thus potentially most affected by errors. We 100
generated ten data sets that were equal to the original one, except that we added a substantial 101
amount of random error to the estimates of body size. The errors were drawn from a normal 102
distribution with standard deviation equal to 10% of the estimated body size. The ten data sets 103
with artificially increased error yielded survival rates that were almost identical to the ones 104
obtained from the original data set. The most extreme value for any survival rate was within 70%
105
of the standard error of the original estimate, and our estimates are therefore robust to errors in 106
age and size determination.
107
Statistical methods 108
We used basic capture-mark-recapture (CMR) methods (Lebreton et al. 1992) to estimate 109
recapture and survival rates. CMR methods allow modelling of the recapture rate (probability that 110
an individual was recaptured or resighted at time i, given that it was alive and in the study area at 111
that time) independently of the survival rate. We can therefore examine factors affecting the 112
recapture rate (e.g. effort in the field) and the survival rate separately, and CMR gives unbiased 113
estimates of survival even if a proportion of the individuals was not observed at every recapture 114
occasion. Mortality here includes both death and permanent emigration. In terms of the 115
population ecology of vipers in our area, death and emigration are essentially equivalent, since 116
we only observed two adult males who successfully moved between populations and there are no 117
other populations nearby where emigrants could establish. Second, we used multi-state 118
extensions of CMR models to calculate reproductive probabilities of females (Nichols et al.
119
1994). CMR models assume that all individuals within one group have the same probability of 120
survival and recapture in each time step, and that all individuals are identified correctly (Lebreton 121
et al. 1992). We verified that our data met these assumptions using a goodness-of-fit test provided 122
by the program RELEASE (Test 2+3, Burnham et al. 1987) and found that a general time 123
dependent model described the data well (each population tested separately: A: χ2= 33.30, df=
124
29, P= 0.27; B: χ2= 25.72, df= 23, P= 0.22; C: χ2= 9.07, df= 6, P= 0.17; D: χ2= 15.51, df= 18, 125
P= 0.63; E: χ2= 15.70, df= 12, P= 0.21; F: χ2= 19.23, df= 17, P= 0.32). The other models are 126
generalisations or simplifications of these models and do therefore also meet the assumptions.
127
We are, however, violating the additional assumption that recaptures are instantaneous in time, 128
and this may lead to overestimating survival. Hargrove and Borland (1994) estimated this bias to 129
be <5% in situations comparable to ours.
130
Because the sample sizes precluded fitting large numbers of models or overly complex 131
models, we limited our analyses to a few factors that seemed most likely on biological grounds, 132
and a minimal number of models. These models form our set of candidate models. Additional 133
models, coming up as interesting alternatives during analysis, were fitted a posteriori and are 134
marked in the tables accordingly. All models were fitted using maximum-likelihood methods 135
implemented in the program MARK (White and Burnham 1999). To compare models we used 136
the sample-size adjusted Akaike's Information Criterion (AICc; Burnham and Anderson 2002).
137
The model with the lowest AICc value is best supported by the data. For each model, we also 138
calculated Akaike weights (w) to assess the relative support from the data for a particular model 139
as compared to the other models in the set (Burnham and Anderson 2002). Model selection 140
identifies the model that best describes the structure in a data set, and favours the model that 141
provides the best balance between overfitting (hence loss of precision) and underfitting (hence 142
bias, see Burnham and Anderson 2002). Like with any statistical method, smaller effects need 143
larger sample sizes to be detected, and smaller data sets therefore tend to select simpler models 144
than large data sets.
145
Modelling and estimation of recapture and survival probabilities. —– We proceeded in 146
three steps. First, we investigated sex- and age-differences, and temporal variation in survival and 147
recapture rates for each of the six populations separately. Second, we analysed differences 148
between populations in age-specific survival and recapture in a single analysis. It turned out that 149
sex effects were always weaker than age effects, with opposite trends across populations. In order 150
to simplify the modelling procedure, we therefore did not examine sex differences at this second 151
step. Third, we related age-specific survival to weather variation, using data provided by 152
MeteoSwiss meteorological stations. An initial analysis with the largest data set (population F) 153
showed that variation in survival and recapture was best represented by positive linear 154
relationships with age, and we used this relationship for the rest of the analysis. As a 155
consequence, estimates for subadults always lay between the estimates for adults and juveniles, 156
and we do not always report the former separately. We also investigated whether recapture effort, 157
i.e. the number of visits to a field site, affected the recapture rate in all populations. If a 158
population was not visited at all in a particular year, the recapture rate was set to zero for that 159
year. Daily mean temperatures were measured at Wynau (UTM coordinates: 626400/233860, 422 160
m above sea level, for populations A to E) and Neuchâtel (563110/205600, 487 m a.s.l., for 161
population F) and monthly precipitation was measured at Balsthal (619250/240860, 502 m a.s.l., 162
for populations A to E) and Yverdon (539840/181450, 433 m a.s.l., for population F). We 163
considered separate models for the effect of winter and active-season weather. The winter effect 164
consisted of the mean temperature measured on the coldest day and the number of days with 165
mean temperature below 0°C. The active-season effect consisted of the linear and quadratic 166
effects of mean daily temperature and mean monthly precipitation between 1 April and 31 167
October. Quadratic effects were included in the active-season effect because snakes may be 168
sensitive to extreme weather conditions at both ends of the scale (e.g., Saint Girons 1952, 1981).
169
Each of the climate effects entered the models either as a main effect or as an interaction with the 170
age effect. As none of the weather variables were significantly correlated with each other, we did 171
not attempt to reduce their number by principal components analysis.
172
Analysis of probability of reproduction. —– We estimated the probabilities for females to 173
reproduce in a given year using multi-state models (Nichols et al. 1994). We defined two states 174
that sexually mature females could assume: gravid versus non-gravid. The transition probabilities 175
between these states were then 1) the probability of becoming gravid in the following year for a 176
currently non-gravid female (ψnr); 2) the probability for a non-gravid female to remain in this 177
condition (1-ψnr); 3) the probability of not being gravid in the following year for a currently 178
gravid female (ψrn); and 4) the probability for a gravid female to be gravid again in the following 179
year (1-ψrn). These transitions are conditional on survival, i.e. an individual has to survive the 180
time interval before it can change its state. We further make the presently untestable assumption 181
that all individuals with a particular state are equally likely to change from one state into the 182
other. The analysis of reproductive probability included only adult individuals, even though some 183
of the individuals classified as 3rd year subadult may have reproduced in rare cases. Due to the 184
large data requirements of multi-state models, we pooled the data of the populations in close 185
proximity to each other (A to E) and only considered the period between 1994 and 1999 during 186
which all these populations were studied simultaneously. Population F yielded enough data to be 187
analysed separately. We examined the effects of temporal variation and active-season weather on 188
both transition probabilities. We did not consider quadratic effects of active-season weather as in 189
the survival analysis because the smaller sample size and the shorter time span did not warrant 190
more complex effects.
191
Matrix population modelling 192
We used Leslie matrices to estimate the sensitivity of the population growth rate (λ) to 193
variation in vital rates. Methods exist to estimate sensitivity from CMR data directly (Nichols et 194
al. 2000). However, with strongly age-dependent survival as in our data set, these methods are 195
not applicable. The matrix entries were the age-specific survival rates taken from the CMR 196
models and reproductive rates (Appendix II). The latter are the product of the probability for 197
females to reproduce, litter size, the sex ratio within the litter, and the survival probability of 198
new-born from birth in late fall until next spring. Whereas the probability of reproducing was 199
also obtained from the CMR models (see above), data on the other components of recruitment 200
could not be estimated from the data directly. We therefore used data obtained from the literature, 201
supported by occasional observations in our study populations. We used a mean litter size of ten, 202
a 1:1 sex ratio (Saint Girons 1952, Flatt and Dummermuth 1993), and set the survival of new- 203
born equal to the survival of juvenile individuals. Due to the uncertainty in the estimate of 204
reproductive rates, we did not further examine variation in this trait. First, we assessed the effects 205
of variation in fitness components on population growth using sensitivity and elasticity analyses 206
(Stearns 1992, Caswell 2001). We calculated 95% confidence limits by generating 1000 matrices 207
with elements drawn from a normal distribution with mean and variance obtained from the logit 208
transformed CMR estimates. After being sorted by their magnitude, the 25th and 975th bootstrap 209
replicates represent the lower and the upper confidence limits. Second, in a retrospective analysis 210
(Caswell 2000), we asked how much of the weather-caused variance in survival during the 211
different life stages contributed to variation in λ. To do this, we used survival rates obtained from 212
the weather-dependent CMR model and multiplied the variances in stage specific survival with 213
the square of the corresponding sensitivities (Caswell 2001). All matrix analyses were performed 214
for the pooled populations A to E and for population F using the S-plus-2000 software package 215
(Insightful Corp., Seattle USA).
216
Results
217
Recapture rates 218
Model selection showed that the recapture probabilities were lower for juvenile than for 219
adult snakes in populations A, C, D and F and varied with recapture effort or time for all 220
populations but D. In no population did the recapture rate differ between the sexes. The estimates 221
ranged from 0.05 to 0.74 in A, 0.25 to 0.90 in B, 0.002 to 0.91 in C, 0.29 to 0.79 in D, 0.27 to 1 222
in E, and from 0 to 0.89 in F.
223
Patterns of survival 224
Model selection showed similar demographic patterns in all populations. AICc favoured 225
the model incorporating age-dependent survival in populations A, B, E, and F (Table 1). Survival 226
was lowest for juveniles, higher for subadults, and highest for adults (Fig. 1). Population C 227
showed a similar pattern, but the confidence intervals for the estimates were large. The best 228
estimate of the relationship in population D was very near zero (Fig. 1). The AICc-selected best 229
models did not include differences between sexes in any population except F. Population F 230
included the effect of sex and the interaction between age and sex, suggesting higher survival for 231
adult females compared to adult males, but equal survival of the juveniles of both sexes (Fig. 1).
232
Survival stayed fairly constant throughout the duration of our study in all populations, and the 233
models accounting for potential time effects were always poorly supported by the data.
234
Comparison between populations 235
We quantitatively compared all populations, A through F, in a single analysis. We used all 236
data collected between 1986 and 2002 while setting the corresponding recapture rate to zero if a 237
population was not sampled in a particular year. The best-supported models accounted for the 238
effects of sampling effort and age on recapture rates (models 2 to 11, Table 2). AICc further 239
showed that recapture rates differed between populations (models 3 to 11, Table 2). Among the a 240
priori models (models 1 to 10, Table 2), AICc selected the one allowing for survival differences 241
between populations and accounting for interactions between age and winter weather (model 8).
242
A close competitor of model 8 was model 2, excluding the effect of winter weather, while the 243
other models were poorly supported. A posteriori, we investigated the role of winter harshness by 244
fitting a reduced winter-weather model including only the effect of the number of days with 245
temperatures below zero. The AICc value of this model was 3.26 units lower and thus 246
considerably better supported by the data than the best a priori model, suggesting that juvenile 247
survival was strongly dependent on winter harshness whereas adult survival was unaffected (Fig.
248 2).
249
Probabilities of reproduction 250
The multi-state models required pooling populations A to E for calculating the probability 251
for females to became gravid, but we were able to examine population F separately. Model 252
selection suggested constant reproductive probabilities over time except that reproducers in 253
population F were more likely to reproduce again after relatively warm and wet summers (model 254
1 and model 5, Table 3). Model 1, suggesting constant reproductive probabilities, was a close 255
competitor to the best model in population F. In populations A to E the probabilities of 256
reproducing in the following year were 0.27 (95% CI: 0.14 / 0.45) for currently non-reproductive 257
females and 0.26 (CI: 0.09 / 0.57) for currently reproducing females. In population F the 258
probabilities of reproducing were 0.40 (95% CI: 0.13 / 0.75) for currently non-reproductive 259
females and 0.60 (CI: 0.36 / 0.80) for currently reproducing females.
260
For populations A to F, reproducing females survived better than non-reproducing ones.
261
Omitting this factor from the best model (model 1, Table 3a) resulted in a poorly fitting model 262
(K= 4, Deviance = 132.608, AICc= 240.999, ∆ AICc= 2.361). For population F, we found no 263
evidence for differential survival between the two types of females (adding this factor to model 5, 264
Table 3b, resulted in a poorly fitting model: K= 7, Deviance = 151.503, AICc= 278.802, ∆ 265
AICc= 2.163).
266
Sensitivity of λλλλ to variation in survival and recruitment 267
The matrix model (Appendix II) yielded an asymptotic population growth rate (λ), i.e. the 268
growth rate once the population has reached a stable age distribution (Caswell 2001), of 0.873 269
(95% confidence interval: 0.811 / 0.936) for the pooled populations A to E and 1.057 (0.943 / 270
1.152) for population F. These estimates show that populations A to E are projected to decrease 271
given the estimated fitness components, whereas population F is projected to stay constant. For 272
all populations, the sensitivity and elasticity analyses consistently showed that population growth 273
was most affected by variation in adult survival and least affected by variation in reproduction 274
(Table 4). However, the retrospective analysis showed that weather affected λ most strongly 275
through the survival of juveniles as weather caused the largest variation in this life stage (Table 276
4).
277
Discussion
278
This study examined the interactive effects of demography and weather on fitness 279
components, and their effect on the growth rate of six populations of a threatened European 280
snake, the asp viper. Despite the large biological differences of the study species, our results 281
reveal the same patterns reported for mammals and birds (Gaillard et al. 1998, Sæther and Bakke 282
2000), suggesting that these patterns may be general for terrestrial vertebrates. Our main finding 283
is that variation in juvenile survival, but not adult survival, was strongly affected by winter 284
temperature. Winter temperature affected population growth rate predominantly through variation 285
in juvenile survival, even though the sensitivity of the population growth rate to juvenile survival 286
was lower than to adult survival.
287
Climatic variation often affects subsets of a population differently, and in such cases its 288
effect on population dynamics depends on the current demographic composition of the 289
population (Leirs et al. 1997, Coulson et al. 2001, Stenseth et al. 2002). For instance, different 290
responses of the sexes and age classes to climatic variation is one of the factors leading to 291
different population dynamics in the otherwise ecologically similar red deer and Soay sheep on 292
Scottish islands (Clutton-Brock and Coulson 2002). If such patterns are common, detailed 293
knowledge of the demography and differential susceptibility of demographic components of a 294
population to climatic variation is crucial for a mechanistic understanding of population 295
dynamics. Despite the extensive literature on snake population ecology (Parker and Plummer 296
1987), there are few data on survival under natural conditions (e.g. Turner 1977, Shine and 297
Charnov 1992, Flatt et al. 1997). This lack of information is one of the major constraints in snake 298
conservation (Dodd Jr. 1993).
299
The results presented here suggest that survival of juvenile asp vipers is more susceptible 300
to harsh winter conditions than are other fitness components. Several factors could lead to these 301
results: differences between age classes could arise because young individuals are less 302
experienced in finding suitable winter quarters than adults. Alternatively, juveniles may be more 303
likely to run out of fat reserves during hibernation than adults. Our results are unlikely to be 304
affected by differential emigration, as our results would imply greater mobility of young snakes 305
in colder winters, which seems unlikely for these ectothermic organisms. Substantial winter 306
losses have also been found in adult garter snakes (Thamnophis sirtalis; winter mortality: 34 to 307
48%; Gregory 1977), and in the European adder (Vipera berus; juvenile mortality: 47.2%, and 308
adult mortality: 18.1%; Viitanen 1967). These estimates are probably biased high, however, as 309
these studies could not account for detection probabilities.
310
In accordance with the general patterns found in long-lived turtles, birds and mammals 311
(Crouse et al. 1987, Pfister 1998, Sæther and Bakke 2000, Gaillard et al. 2000), population 312
growth in our asp viper populations was less sensitive to changes in the more variable juvenile 313
survival than the less variable adult survival. Yet, winter weather affected population growth 314
predominantly through juvenile survival because it caused most of the variation in this trait. This 315
is consistent with the finding that ungulate population dynamics are mostly driven through 316
variation in juvenile survival despite the relatively low impact of this fitness component on 317
population growth (Gaillard et al. 2000).
318
Our age-specific estimates of survival compare well with earlier estimates on this or 319
similar species (Parker and Plummer 1987; see also discussion in Flatt et al. 1997). For example, 320
Flatt et al. (1997) found an average adult survival rate of 0.75 for populations A and B over the 321
first six and nine years of the study. Our corresponding estimates are 0.74 for populations A to E, 322
and 0.84 for population F. However, as in our previous study (Flatt et al. 1997), we were unable 323
to detect temporal variation in survival of adult vipers. In contrast, the studies by Brown and 324
Parker (1984) and Forsman (1995) have found substantial variation in survival among years. This 325
result potentially is affected by variable recapture success, for which these studies did not correct.
326
While it generally appears that juvenile and first-year mortality is higher than adult 327
mortality among snakes (Saint Girons 1957, Brown and Parker 1984), there is little data on 328
survival of young age classes, and to our knowledge only one study accounted for the possibly 329
lower detection probabilities of young snakes (Stanford 2002). Viitanen (1967) found lower 330
survival in juveniles as compared to adult V. berus, and Saint Girons (1957) estimated a mortality 331
of over 50% in V. aspis during their first months of life. Consistent with this, Jayne and Bennett 332
(1990) and Stanford (2002) found that larger body size positively affects survival in garter 333
snakes, Forsman (1993) demonstrated size-dependent differences in survival of V. berus, and 334
Baron et al. (1996) showed variation in age-specific survival for Vipera ursinii. In our study, we 335
used body size at first encounter as a measure of age and assumed similar growth rates for all 336
snakes during the first four years of their life. We can therefore not strictly distinguish between 337
age effects and size effects. However, our results are mainly based on contrasts between juveniles 338
and adults, the two life stages least sensitive to these assumptions. If anything, inaccuracies in 339
age determination and variation in growth rate would have led to underestimated age effects, and 340
our results are thus conservative. We further found that potential errors in size determination had 341
a negligible effect on our results.
342
Based on observations that did not take into account variation in detection probabilities, 343
Saint Girons (1952, 1957) argued that female vipers reproduce every two to four years. Using the 344
multi-state model, we could quantify the breeding probability and found that the estimated annual 345
probability for females to become gravid ranged from 26% to 60% in our study populations. This 346
result suggests that females reproduced on average every second to fourth year (see also Flatt and 347
Dummermuth 1993), even though the confidence intervals around these estimates were relatively 348
large. Interestingly, the probability of reproducing did not depend on whether a female had 349
reproduced in the year before or not. This result contrasts with estimates from an asp viper 350
population in western France, where females reproduce only after having reached a certain 351
threshold in body condition, and most of the females were found to reproduce only once in their 352
life-time (Naulleau and Bonnet 1996, Lourdais et al. 2002, Bonnet et al. 2002). We found at least 353
two females that were gravid in four consecutive years. Furthermore, we found no evidence for 354
reduced survival of reproductive females. If anything, they had higher survival than non- 355
reproducers. The difference between these studies suggests that there is considerable geographic 356
variation in life history of Vipera aspis (see also discussion in Moser et al. 1984).
357
The effects of weather and microclimatic conditions on many aspects of the ecology of 358
terrestrial ectothermic vertebrates such as reptiles is well studied (e.g., Moser et al. 1984, 359
Peterson et al. 1993, Daltry et al. 1998, Flatt et al. 2001, Sun et al. 2001, Lourdais et al. 2004, and 360
references therein), yet linking this knowledge to population dynamics requires detailed 361
demographic models. So far, the precise demographic data required to parameterise such models 362
are rare for reptiles and amphibians (but see Flatt et al. 1997, Anholt et al. 2003). This is partly 363
due to the difficulty of observing these mostly secretive and less active ectotherms. Here we 364
present such a demographic model for the asp viper. While our data permitted us to model age- 365
specific survival, we could not observe reproduction frequently enough to analyse the effects of 366
weather on variation in reproductive output. Nevertheless, our study is a step towards a better 367
understanding of the factors driving the population dynamics of ectothermic vertebrates. For 368
instance, many Swiss populations of the asp viper have been declining, with some populations 369
going extinct (Moser et al. 1984, Monney 2001). Except for habitat destruction, the factors 370
driving the decline or extinction are typically unknown. Only long-term ecological field studies 371
based on large numbers of populations and individuals can unravel the underlying causes of such 372
changes in population dynamics. Our study suggests that a complex interplay between climatic 373
variation and demography may be important for the population dynamics of ectothermic 374
vertebrates.
375
Acknowledgements — We thank M.T. Miller for advice with the matrix models, S.J.
376
Downes and R. Shine for useful references and discussion, and B. Erni, P. Govindarajulu, P.T.
377
Gregory, M. Kéry, B. Schmidt, M. Voordouw, and two anonymous reviewers for valuable 378
comments on a previous version of the manuscript. Weather data were kindly provided by the 379
Swiss Federal Office of Meteorology and Climatology (MeteoSwiss). TF was supported by the 380
Swiss Study Foundation and the Roche Research Foundation, and TF and RA were supported by 381
the Swiss Nationalfonds (grants no. 81ZH-68483 to RA and no. 3100-053601.98 to T.J.
382
Kawecki).
383
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Table 1. Model selection for survival of asp vipers in six populations (A to F) in northern Switzerland. The selected models for the recapture probability included the effects of sampling effort (A, B, C), age (A, C, D), time (E), and simultaneous effects of age, time and their
interaction (F) (model selection for recapture not shown). The fit of the models is assessed by Akaike's Information Criterion (AICc); lower values indicate better fit. ∆AICc gives the difference in AICc between each model and the best model (in bold). The Akaike weights (w) assess the relative support that a given model has from the data, compared to the other models in the set. K is the number of estimated parameters of a given model. The Deviance is the difference in -2 log Likelihood between each model and the saturated model, the saturated model being the one with the number of parameters equal to the sample size.
Population (recapture)
Factors in survival model
K Deviance AICc ∆ AICc w
A constant 4 216.276 258.957 1.192 0.244
(age, effort) time 14 209.912 276.430 18.665 0.000
age 5 212.897 257.765 0.000 0.443
sex 5 216.260 261.128 3.363 0.082
sex, age 6 212.532 259.628 1.863 0.174
sex, age, interaction 7 212.517 261.881 4.116 0.057 Σ= 1
B constant 3 166.067 199.409 6.154 0.025
(effort) time 13 149.595 207.768 14.513 0.000
age 4 157.709 193.255 0.000 0.535
sex 4 164.448 199.994 6.739 0.018
sex, age 5 156.539 194.345 1.090 0.310
sex, age, interaction 6 156.272 196.395 3.140 0.111 Σ= 1
C constant 4 76.158 103.687 0.000 0.493
(age, effort) time 14 74.952 132.181 28.494 0.000
age 5 75.105 105.058 1.371 0.248
sex 5 76.030 105.983 2.296 0.156
sex, age 6 75.087 107.565 3.878 0.071
sex, age, interaction 7 74.056 109.168 5.481 0.032 Σ= 1 D constant 3 128.738 215.877 0.000 0.477
(age) time 10 122.418 225.574 9.697 0.004
age 4 128.737 218.032 2.155 0.162
sex 4 128.026 217.321 1.444 0.232
sex, age 5 127.995 219.488 3.611 0.078
sex, age, interaction 6 126.766 220.500 4.623 0.047 Σ= 1
Table 1, continued.
Population Factors in survival model
K Deviance AICc ∆ AICc w
E constant 8 121.764 264.84 10.160 0.004
(time) time 13 119.01 273.741 19.061 0.000
age 6 116.039 254.68 0.000 0.646
sex 7 121.659 262.502 7.822 0.013
sex, age 7 115.736 256.579 1.899 0.250
sex, age, interaction 8 115.612 258.687 4.007 0.087 Σ= 1
F constant 11 216.600 523.450 13.505 0.001
time 14 213.171 526.599 16.654 0.000
(age, time,
interaction) age 12 206.225 515.252 5.307 0.043
sex 12 208.488 517.515 7.570 0.014
sex, age 13 199.942 511.162 1.217 0.332
sex, age, interaction 14 196.517 509.945 0.000 0.610 Σ= 1
Table 2. Model selection for the comparison between six populations of the asp viper in northern Switzerland. Effort = number of visits to a site per season. Models 7 to 11 examine the effects of weather on survival: winter = minimum temperature and number of days below zero, active season = mean daily temperature between 1 April and 31 October and mean precipitation over the same period (both effects linear and quadratic). Only the a priori models were included in the calculation of w, and ∆ AICc is the difference in AICc to the best a priori model. * between two effects symbolises interactive effects; ‡ post hoc model including the number of days below zero only. See also legend to table 1.
Factors in survival model Factors in recapture model
K Deviance AICc ∆ AICc w
1 population, age population, age, time 29 757.040 1557.423 8.190 0.007 2 population, age population, age, effort 15 778.667 1549.485 0.252 0.346 3 population, age age, effort 10 795.751 1556.252 7.019 0.012 4 age population, age, effort 10 794.074 1554.575 5.342 0.027 5 population population, age, effort 14 804.809 1573.554 24.321 0.000 6 population * age population, age, effort 20 774.124 1555.386 6.153 0.018 7 population, age, winter population, age, effort 17 775.896 1550.876 1.643 0.173 8 population, age * winter population, age, effort 19 770.070 1549.233 0.000 0.393 9 population, age, active
season
population, age, effort
19 776.126 1555.288 6.055 0.019 10 population, age * active
season
population, age, effort
23 769.912 1557.501 8.268 0.006 11 ‡ population, age * days
below zero
population, age, effort
17 770.997 1545.977 -3.256
Σ= 1
Table 3. Model selection for multi-state models examining the probability of asp vipers to reproduce in populations A to E (a, n=51 females), and F (b, n=34 females). We included data collected between 1994 and 1999 for populations A to E, and data collected between 1987 and 1992 for population F. For both data sets the most parsimonious model included constant survival and recapture rates, except that reproducers survived better than non-reproducers in populations A to E (model selection for these components not shown). K is the number of structural
parameters, which were all estimable for the best-supported models. See also legend to table 1.
Currently not reproducing (ψnr)
Currently
reproducing (ψrn)
K Deviance AICc ∆ AICc w
a) Populations A to E
1 constant constant 5 127.977 238.638 0.000 0.522
2 time constant 9 119.854 240.225 1.587 0.236
3 constant time 9 124.127 244.498 5.860 0.028
4 active-season constant 7 125.880 241.265 2.627 0.140 5 constant active season 7 127.192 242.576 3.938 0.073
Σ= 1
b) Population F
1 constant constant 4 156.853 277.373 0.734 0.249
2 time constant 8 153.440 283.096 6.457 0.014
3 constant time 8 151.249 280.904 4.265 0.043
4 active season constant 6 156.739 281.730 5.091 0.028 5 constant active season 6 151.648 276.639 0.000 0.360
Σ= 1
Table 4. Sensitivity (with 95% confidence limits) and elasticity of the population growth rate (λ) of asp vipers in northern Switzerland to variation in fitness components. Both analyses ask by how much growth rate is changed by a certain change in a fitness component. The former considers absolute changes, whereas the latter considers proportional changes and is thus better suited to compare traits that are measured at different scales. The elasticities sum to one over the whole life cycle. The retrospective analysis (RA) asks how much the observed variance in survival, caused by winter weather, contributed to variance in λ, and is given in % relative to the other survival rates. Sample sizes for the retrospective analysis were 16 years for the pooled populations A-E and five years for population F.
Populations A-E Population F
Sensitivity Elasticity RA Sensitivity Elasticity RA
Juvenile survival 0.193
(0.128/0.266) 0.094 61.3 0.206
(0.128/0.273) 0.114 44.0 1st year subadult
survival
0.159 (0.107/0.210)
0.094 28.3 0.180 (0.112/0.233)
0.114 24.0 2nd year subadult
survival
0.136 (0.093/0.179)
0.094 9.4 0.162 (0.101/0.206)
0.114 12.0 3rd year subadult
survival 0.120
(0.080/0.155) 0.094 < 1 0.148
(0.093/0.187) 0.114 4.0
Adult survival 0.629 (0.548/0.728)
0.531 < 1 0.558
(0.477/0.695)
0.430 16.0 Reproduction* 0.092
(0.063/0.138) 0.094 0.100
(0.061/0.181) 0.114
* reproduction is the product of the probability of reproducing, litter size, sex ratio within litter, and survival of new-born until the spring after birth.
Figure 1. Age specific survival in six populations of asp vipers in northern Switzerland.
The estimates are taken from the age specific model for populations A to E, and from the model with interacting age and sex effects for population F. The error bars show the 95% confidence interval, which is derived from the linear predictors, on the logit scale. The symbols are slightly offset for ease of interpretation.
Figure 2. Interaction between winter harshness, expressed as the number of days with average temperatures below zero, and age on survival of asp vipers. The figure shows estimates for population B, which has been studied over the longest time. Estimates for the other
populations differ from those shown by a constant value. The vertical lines show the 95%
confidence interval, which is derived from the linear predictors, on the logit scale. Estimates from model 11, Table 2.
Figure 1.
1 2 3 4 5
0.0 0.2 0.4 0.6 0.8 1.0
A B C D
1 2 3 4 5
E
F females F males
A n n u al s u rv iv al r a te
Age [years]
+ +
Figure 2
Days below zero
A n n u al s u rv iv al r a te
20 30 40 50 60
0.0 0.2 0.4 0.6 0.8 1.0
Adults
Juveniles
Appendix I
Number of captures/resightings (number of newly encountered individuals in parenthesis) in six populations (A to F) of Vipera aspis over the years of the study. Total number of captures/resightings is given for each population and year (number of new individuals for each year, and total numbers of individuals per population in parenthesis).
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Total
A 5
(5) 8 (6)
5 (3)
16 (13)
21 (11)
16 (7)
10 (5)
10 (1)
7 (2)
3 (1)
4 (2)
6 (4)
4 (2)
1 (0)
116 (62) B 3
(3) 8 (6)
7 (2)
1 (0)
4 (1)
5 (4)
3 (1)
8 (7)
6 (4)
5 (0)
5 (0)
3 (0)
7 (3)
10 (5)
5 (0)
5 (4)
5 (1)
90 (41)
C 3
(3) 5 (4)
5 (2)
6 (2)
6 (5)
6 (2)
5 (1)
6 (3)
5 (1)
7 (4)
1 (0)
2 (1)
57 (28)
D 9
(9)
17 (12)
13 (6)
8 (2)
6 (2)
18 (13)
13 (4)
25 (16)
13 (2)
122 (66)
E 2
(2)
22 (20)
20 (5)
35 (19)
36 (16)
21 (6)
14 (7)
17 (7)
167
(82)
F 49
(49) 81 (50)
64 (16)
55 (11)
41 (7)
33 (3)
323
(136) 3
(3)
57 (55)
88 (52)
70 (21)
67 (18)
54 (17)
59 (23)
56 (40)
57 (27)
73 (41)
70 (25)
44 (11)
36 (16)
54 (28)
31 (12)
35 (22)
21 (4)
875 (415)
Notes: Populations A-E are located near Solothurn (coordinates: 607067/229174) and F is in Vaud, near Neuchâtel (coordinates: 563110/205600). Because the asp viper is a threatened and protected species, we do not give here the exact coordinates and locations of our study sites. Site A (approx. 4.6 km from Solothurn) lies on a SSE facing slope 800 to 900 m above sea level. The most important area of this site is a stretch approximately 600 m long and 100 m wide that includes areas covered with stones and small boulders as well as forested sections (see Flatt and Dummermuth 1993). Site B (approx. 4.9 km from Solohthurn) lies on a SE facing rocky forested ridge, approximately 700 ml long and 100 m wide, at an altitude of 800 to 920 m above sea level.
The ridge runs out into a steep rocky slope at the south-eastern end. Site C (approx. 5 km from Solothurn) consists of a S to SSE-facing rocky ridge and adjacent boulder and talus strewn areas between two quarries at an altitude of 710 to 740 m above sea level and measures approximately 100 x 60 m. Site D (approx. 8 km from Solothurn) is a stretch approximately 500 m long and 150 to 200 m wide on a rocky ridge facing S to SE. Forested areas intersect talus and rocky areas.
With an altitude of 860 to 1’060 m above sea level site D is one of the most elevated viper habitats in northern Switzerland. Site E (approx. 18.5 km from Solothurn) lies on an altitude of 519 to 686 m above sea level and covers a S to SSE facing forested slope interspersed with rock walls and talus areas. The site covers a surface of approximately 1000 x 150 m. Site F (approx.
22 km from Neuchâtel) covers an area of about 6 ha, is mainly SSE facing and lies at an altitude of 429 to 475 m above sea level. Half of the surface of this site is covered by oak groves. Most vipers live in an old abandoned quarry in the centre of the site and on adjacent talus slopes.
Appendix II
Population projection matrix (with 95% confidence limits) for populations A to E:
) (
744 . 0 )
(
671 . 0 0
0 0
0 ) 0
(
591 . 0 0
0
0 0
) 0 (
506 . 0 0
0 0
0 ) 0
(
420 .
0 ( )
923 . 0 0
0 0
0
2 0.703/0.78 0
0.628/0.71 5
0.534/0.64 7
0.418/0.58 4
0.308/0.54
0 0.423/1.56
Population projection matrix (with 95% confidence limits) for population F:
) (
841 . 0 )
(
792 . 0 0
0 0
0 ) 0
(
727 . 0 0
0
0 0
) 0 (
655 . 0 0
0 0
0 ) 0
(
574 . 0
) (
323 . 0 1
0 0
0
5 0.784/0.88 9
0.735/0.83 7
0.660/0.78 8
0.564/0.73 1
0.457/0.68
1 0.412/2.33
